David Israel Diaz-Jimenez ("Diaz") petitions for review of the decision of the Board of Immigration Appeals ("BIA") upholding his order of removal. The Immigration Judge ("IJ") concluded that Diaz was removable because he made a false claim of United States citizenship to obtain private employment, in violation of 8 U.S.C. § 1182(a)(6)(C)(ii)(I) of the Immigration and Nationality Act ("INA"). The BIA dismissed Diaz's appeal, writing that "an alien who represents himself as a citizen on a Form I-9 to secure employment with a private employer has falsely represented himself for a purpose or benefit under the Act." There is no basis in the record for concluding that Diaz "represent[ed] himself as a citizen on a Form I-9." Because we conclude that removability under § 1182(a)(6)(C)(ii)(I) because of a false representation for a "purpose or benefit" under 8 U.S.C. § 1324a must be based on such a representation on a Form I-9, we grant Diaz's petition for review and remand for further proceedings.
I. Background
Diaz is a native and citizen of Mexico. In July 2013, he was served a Notice to Appear ("NTA"), alleging illegal entry into the United States on or about September 15, 1993. The NTA charged four grounds of removal: (1) under 8 U.S.C. § 1182(a)(6)(A)(i), for being present in the United States without having been admitted or paroled, or for having arrived in the United States at a "time or place other than as designated by the Attorney General"; (2) under § 1182(a)(6)(C)(ii)(I), for "falsely represent[ing]" himself to be a citizen of the United States for a "purpose or benefit" under federal or state law; (3) under § 1182(a)(2)(A)(i)(I), for being convicted of a crime involving moral turpitude; and (4) under § 1182(a)(6)(C)(i), for seeking to procure a benefit under the INA "by fraud or willfully misrepresenting a material fact."
Diaz conceded before an IJ that he was removable under the first ground, but denied removability under the others. The IJ held that Diaz was removable under the first and second charges-unlawful entry and false claim of citizenship. The IJ refused to sustain the third charge-conviction of a crime involving moral turpitude. Finally, the IJ wrote that it "necessarily follow[ed]" from the second charge that Diaz was inadmissible under the fourth *958charge-fraudulent or willful misrepresentation for a benefit under the INA. The IJ denied Diaz's application for voluntary departure.
Diaz appealed to the BIA, contending that the IJ had erred in concluding that he was removable under § 1182(a)(6)(C)(ii)(I) for making a false representation of citizenship for a purpose or benefit under state or federal law. The BIA dismissed Diaz's appeal. It wrote:
[Diaz's] sole contention is that he is not removable pursuant to section 212(a)(6)(C)(ii) of the Act, 8 U.S.C. § 1182(a)(6)(C)(ii), inasmuch as a false claim to United States citizenship to obtain employment does not fall with[in] the statute. However, the Board held subsequent to the hearing that an alien who represents himself as a citizen on a Form I-9 to secure employment with a private employer has falsely represented himself for a purpose or benefit under the Act. See Matter of Bett , 26 I&N Dec. 437 (BIA 2014).
The BIA noted that the IJ had not sustained the third charge, and concluded that the IJ had not ruled on the fourth charge.
Diaz's only contention before us is that the BIA erred in upholding the IJ's decision that he was removable under § 1182(a)(6)(C)(ii)(I). He concedes that he is removable under § 1182(a)(6)(A)(i) (unlawful entry). However, his petition is not moot because different and more severe consequences flow from being found removable under § 1182(a)(6)(C)(ii)(I) (false claim of citizenship).
II. Standard of Review
"We review the BIA's legal determinations de novo and its factual findings for substantial evidence." Kyong Ho Shin v. Holder , 607 F.3d 1213, 1216 (9th Cir. 2010).
III. Discussion
The section of the INA at issue, 8 U.S.C. § 1182(a)(6)(C)(ii)(I), provides:
Any alien who falsely represents, or has falsely represented, himself or herself to be a citizen of the United States for any purpose or benefit under this chapter (including section 1324a of this title) or any other Federal or State law is inadmissible.
Before the IJ and in his brief to the BIA, Diaz principally argued that private employment is not a "purpose or benefit" within the meaning of § 1182(a)(6)(C)(ii)(I). Diaz also argued to the BIA, in the alternative, that a false representation of citizenship under § 1182(a)(6)(C)(ii)(I) for the purpose of obtaining private employment requires that the representation be made "under penalty of perjury" on a "designated or established" form, as provided under 8 U.S.C. § 1324a(b)(2). As described above, the BIA responded that "an alien who represents himself as a citizen on a Form I-9 to secure employment with a private employer has falsely represented himself for a purpose or benefit under the Act."
Diaz makes both arguments to us. We discuss them in turn.
A. Private Employment as a "Purpose or Benefit" under the INA
Diaz argues that private employment is not a "purpose or benefit" within the meaning of § 1182(a)(6)(C)(ii)(I). We disagree.
If § 1182(a)(6)(C)(ii)(I) referred only to a "purpose or benefit under ... Federal or State law," we would conclude that "purpose or benefit" does not include private employment. However, § 1182(a)(6)(C)(ii)(I) contains an additional clause-"(including section 1324a of this title)"-specifying a particular "purpose or *959benefit" that would not otherwise have been within the scope of the statute. "[S]ection 1324a of this title" refers to 8 U.S.C. § 1324a, entitled "Unlawful employment of aliens."
Section 1324a makes it unlawful to knowingly hire an "unauthorized alien." 8 U.S.C. § 1324a(a)(1)(A). An "unauthorized alien" is an alien who at the time of employment is neither lawfully admitted for permanent residence nor authorized to work in the United States. Id. § 1324a(h)(3). Section 1324a requires employers to screen for unauthorized aliens using an "[e]mployment verification system." Id. § 1324a(b) ; see H.R. Rep. No. 99-1000, at 88 (1986) (Conf. Rep.). Section 1324a covers federal employment, see 8 U.S.C. § 1324a(a)(7), but its principal concern is private employment.
We conclude that by specifically referencing § 1324a in the text of § 1182(a)(6)(C)(ii)(I), Congress expressed an intent to make private employment a qualifying "purpose or benefit." In so concluding, we join other circuits that have reached the same conclusion. See, e.g. , Rodriguez v.Mukasey , 519 F.3d 773, 777 (8th Cir. 2008) (holding that "the explicit reference to § 1324a in § 1182(a)(6)(C)(ii)(I) indicates that private employment is a 'purpose or benefit' of the Act"); see also Dakura v. Holder , 772 F.3d 994, 999 (4th Cir. 2014) (collecting cases). The BIA also so concluded in Matter of Bett , 26 I. & N. Dec. 437, 440 (BIA 2014), holding that "an alien who represents himself as a citizen on a Form I-9 to secure employment with a private employer has falsely represented himself for a purpose or benefit under the Act."
B. False Representation of Citizenship under § 1324a
Diaz further argues that even if private employment qualifies as a "purpose or benefit," he has not made a false representation of citizenship for purposes of § 1324a. Section 1324a(b)(2) provides:
Individual attestation of employment authorization
The individual [seeking employment] must attest, under penalty of perjury on the form designated or established for purposes of paragraph (1), that the individual is a citizen or national of the United States, an alien lawfully admitted for permanent residence, or an alien who is authorized under this chapter or by the Attorney General to be hired, recruited, or referred for such employment. Such attestation may be manifested by either a hand-written or an electronic signature.
8 U.S.C. § 1324a(b)(2). No other subsection of § 1324a imposes an obligation on a person seeking employment, and no other subsection refers to a representation of citizenship. Diaz argues that he is removable under § 1182(a)(6)(C)(ii)(I) only if he made a false representation of citizenship on "the form designated or established" under § 1324a(b)(2). For the reasons that follow, we agree.
1. Exhaustion Before the BIA
Before reaching the merits of Diaz's argument, we must determine whether he has "exhausted all administrative remedies available ... as of right." Puga v. Chertoff , 488 F.3d 812, 815 (9th Cir. 2007) (quoting 8 U.S.C. § 1252(d)(1) ). To satisfy the exhaustion requirement, Diaz needed to "put the BIA on notice" in his appeal from the IJ's removal order. Ren v. Holder , 648 F.3d 1079, 1083 (9th Cir. 2011) (quoting Moreno-Morante v. Gonzales , 490 F.3d 1172, 1173 n.1 (9th Cir. 2007) ).
"We do not employ the exhaustion doctrine in a formalistic manner." Id. (quoting Figueroa v. Mukasey , 543 F.3d 487, 492 (9th Cir. 2008) ). Thus, while "[a]
*960petitioner cannot satisfy the exhaustion requirement by making a general challenge" to the BIA's decision, the petitioner "need not ... raise the precise argument below." Garcia v. Lynch , 786 F.3d 789, 793 (9th Cir. 2015) (per curiam) (emphasis in original) (quoting Vizcarra-Ayala v. Mukasey , 514 F.3d 870, 873 (9th Cir. 2008) ). For example, in Moreno-Morante , an alien sought to argue before this court that grandchildren meet the definition of "child" under 8 U.S.C. § 1101(b)(1)(F)(i). 490 F.3d at 1173 n.1. The alien had not made this precise statutory argument to the BIA, arguing only that grandchildren should be considered qualifying relatives for purposes of cancellation of removal. Id. We held that the alien had given the agency "an opportunity to pass on this issue," id. (quoting Zhang v. Ashcroft , 388 F.3d 713, 721 (9th Cir. 2004) (per curiam) ), and that his "failure to elaborate on his general contention with a specific statutory argument is ... immaterial." Id.
We conclude that Diaz has satisfied the exhaustion requirement. In his brief to the BIA, he contested his removability under § 1182(a)(6)(C)(ii)(I), writing, "[T]he purpose of this legal brief is to determine if the respondent's false claim to U.S. Citizenship for employment makes him inadmissible and hence, removable." Diaz principally argued that private employment was not a "purpose or benefit" within the meaning of the section. However, he also pointed out that "the purpose of [ § 1324a ] is to make it: '... unlawful for a person or other entity to hire ... an alien, knowing the alien is an unauthorized alien.' This applies only to employers, not to unlawful aliens." He specifically noted that § 1324a(b)(2)"is the only wording in section [1324a] that places any liability on an unauthorized alien." Diaz did not make the precise argument we now consider, but he gave the BIA an adequate opportunity to pass on the issue. We therefore consider the argument on the merits.
2. False Representation of Citizenship
Section 1324a(b)(2) requires a person seeking employment to attest to United States citizenship on "the form designated or established" for that purpose. Diaz argues that an alien can make a false representation of citizenship under § 1324a(b)(2) only by making the false representation on that form.
"[T]he starting point for interpreting a statute is the language of the statute itself. When interpreting a statute, we first use the traditional tools of statutory construction to determine whether Congress directly addressed the precise question at issue. If the precise question at issue is addressed, then the unambiguously expressed intent of Congress controls. A 'clear and unambiguous' statutory provision is one in which the meaning is not contradicted by other language in the same act." Olympic Forest Coal. v. Coast Seafoods Co. , 884 F.3d 901, 905 (9th Cir. 2018) (internal citations and quotation marks omitted).
Section 1182(a)(6)(C)(ii)(I) applies to an alien who makes a false representation of citizenship "under this chapter (including section 1324a of this title)." To interpret this provision, "we must read the words in their context and with a view to their place in the overall statutory scheme." King v. Burwell , --- U.S. ----, 135 S.Ct. 2480, 2489, 192 L.Ed.2d 483 (2015) (internal quotation marks omitted). Context is especially important for words like "under," which can have a variety of meanings. See Kucana v. Holder , 558 U.S. 233, 245, 130 S.Ct. 827, 175 L.Ed.2d 694 (2010) ("The word 'under' is chameleon; it has many dictionary definitions and must draw its meaning from its context." (internal quotation marks omitted) ).
Section 1182 uses the word "under" in several places. For example, the statute *961speaks of "aliens who are inadmissible under the following paragraphs," 8 U.S.C. § 1182(a), and children "seeking an immigrant visa as an immediate relative under section 1151(b) of this title," id. § 1182(a)(1)(C)(iii). The statute also defines "terrorist activity" as "any activity which is unlawful under the laws of the place where it is committed." Id. § 1182(a)(3)(B)(iii).
These uses of "under" consistently reflect the meaning "in accordance with." Kirtsaeng v. John Wiley & Sons, Inc. , 568 U.S. 519, 530, 133 S.Ct. 1351, 185 L.Ed.2d 392 (2013) (quoting 18 Oxford English Dictionary 950 (2d ed. 1989) ). To qualify "under" a statutory provision, the regulated person or act must satisfy the criteria specified by the provision. For example, to be "inadmissible under" § 1182, an alien must fit within one of the described classes of inadmissible aliens. Similarly, to be "unlawful under the laws of the place" where an activity is committed, the activity must be prohibited by the terms of a law of the local jurisdiction. See Zumel v. Lynch , 803 F.3d 463, 473 (9th Cir. 2015) ("The relevant inquiry under § 1182(a)(3)(B)(iii) is whether the activity is unlawful ...." (emphasis removed) ). With this in mind, we consider the text of § 1324a.
The obligations imposed by § 1324a fall almost entirely on employers. See, e.g. , 8 U.S.C. § 1324a(a) ("[m]aking employment of unauthorized aliens unlawful"). Employers must "attest, under penalty of perjury," that they have verified their new hires. Id. § 1324a(b)(1)(A). Employers "must ensure that the individual [employee] properly" completes his or her section of the Form I-9, and must review documentation establishing an employee's identity and work authorization and "ensure that the documents presented appear to be genuine and ... relate to the individual." 8 C.F.R. § 274a.2(b)(1). The employer must also complete the "Employer Review and Verification" section of the Form I-9. Id. Employers who engage in a pattern or practice of violating the verification system are subject to criminal penalties. See 8 U.S.C. § 1324a(f)(1) (imposing fines "for each unauthorized alien with respect to whom such a violation occurs").
Section 1324a imposes a single requirement on employees: "The individual must attest, under penalty of perjury on the form designated or established for purposes of paragraph (1) , that the individual is a citizen or national of the United States, an alien lawfully admitted for permanent residence, or an alien who is authorized under this chapter or by the Attorney General to be hired, recruited, or referred for such employment." Id. § 1324a(b)(2) (emphasis added). The "designated or established" form is Form I-9. See 8 C.F.R. § 274a.2(a)(2).
We easily conclude from the foregoing that making a false representation of United States citizenship on a Form I-9 qualifies as a false representation "under ... section 1324a of this title." Our sister circuits that have considered this question agree. See Ferrans v. Holder , 612 F.3d 528, 530 (6th Cir. 2010) (noting that "Ferrans falsely represented himself to be a United States citizen on an Employment Eligibility Verification Form ('Form I-9') in order to obtain employment at Jiffy Lube"); Rodriguez , 519 F.3d at 777 ("[W]e hold that an alien who marks the 'citizen or national of the United States' box on a Form I-9 for the purpose of falsely representing himself as a citizen to secure employment with a private employer has falsely represented himself for a benefit or purpose under the Act."); Kechkar v. Gonzales , 500 F.3d 1080, 1082 (10th Cir. 2007) ("DHS later added a charge of misrepresenting United States citizenship. Regarding the added charge, DHS alleged that Kechkar had, on February 6, 2002, completed *962an employment-eligibility verification form (Form I-9) to work for Dillard's, Inc.").
The precise question before us, however, is different. The question is whether making a false representation on a Form I-9 is the only false representation of citizenship to procure private employment that qualifies as a false representation under § 1182(a)(6)(C)(ii)(I).
We are assisted in answering the question by the BIA's decision in Matter of Bett , where the BIA held that "an alien who represents himself as a citizen on a Form I-9 to secure employment with a private employer has falsely represented himself for a purpose or benefit under the Act." 26 I. & N. Dec. at 440 (emphasis added). In support of its conclusion, the BIA cited four decisions from different circuits. Id. Three of them were the decisions cited above, all of which addressed private employment obtained through a false representation of citizenship on a Form I-9. See Ferrans , Rodriguez , and Kechkar , supra . The fourth was Castro v. Attorney General of the U.S. , 671 F.3d 356 (3d Cir. 2012), in which the court held that avoiding the attention of the immigration authorities did not qualify as a "purpose or benefit" under § 1182(a)(6)(C)(ii)(I). Castro did not involve private employment, but in the course of its analysis the court summarized the legislative history of § 1182(a)(6)(C)(ii)(I). The Castro court concluded, "There is no question that § 1182(a)(6)(C)(ii) encompasses false claims of U.S. citizenship made during the employment eligibility verification process." Id. at 369.
Further, in its Bett opinion, which contains a thorough discussion of inadmissibility under § 1182(a)(6)(C)(ii)(I), the BIA sustained the charge against Bett based only on his false representation of citizenship on a Form I-9. Bett had also presented an altered social security card as part of his application for employment, but the BIA considered this irrelevant. Although the altered card could be considered in assessing Bett's credibility, the BIA concluded that "altered social security cards are not evidence of a false claim to citizenship." Bett , 26 I. & N. Dec. at 443.
We are further assisted by the legislative history of § 1182(a)(6)(C)(ii)(I), which reflects a narrow focus on false representations under § 1324a(b)(2). The reference to § 1324a was added as an amendment to § 1182(a)(6)(C)(ii)(I) to penalize false attestations of citizenship under § 1324a(b)(2). 142 Cong. Rec. 10,030 (1996). Senator Alan Simpson explained that he introduced the amendment in response to the "obvious weakness" of the attestation system, namely, "the potential for false claims of citizenship" by persons seeking employment. Id. According to Senator Simpson, the amendment addressed this weakness by "creating a new disincentive for falsely claiming U.S. citizenship, which will be a new ground of exclusion and of deportation." Id.
Considering the language of § 1182(a)(6)(C)(ii)(I), the BIA's decision in Matter of Bett , and the legislative history, we conclude that an alien can violate § 1182(a)(6)(C)(ii)(I) by a false representation of citizenship for the "purpose or benefit" of obtaining private employment under § 1324a only when such a representation is made under § 1324a(b)(2) on a Form I-9. We emphasize that while a false representation of citizenship for a purpose or benefit under § 1324a must be on a Form I-9, this is not so for false representations for other purposes or benefits under other laws. See , e.g. , Valadez-Munoz v. Holder , 623 F.3d 1304, 1308-09 (9th Cir. 2010) (presentation of a false birth certificate in order to gain admission into the United States).
*963Conclusion
There is nothing in the record showing that Diaz ever filled out a Form I-9. There is therefore nothing in the record to show that he made a false representation of citizenship under § 1324a(b)(2), and that, as a consequence, he made a false representation of citizenship within the meaning of § 1182(a)(6)(C)(ii)(I).
We grant the petition for review and remand for further proceedings.
Petition GRANTED and REMANDED.